Geodesic
Strong chromatic index of claw-free graphs with edge weight seven
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 4, pp. 1311-1325

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Let G be a graph and k a positive integer. A strong k-edge-coloring of G is a mapping ϕ: E(G)→{1,2,...,k} such that for any two edges e and e^' that are either adjacent to each other or adjacent to a common edge, ϕ(e)ϕ(e^'). The strong chromatic index of G is the minimum integer k such that G has a strong k-edge-coloring. The edge weight of G is defined to be max{d(u)+d(v):uv∈ E(G)}, where d(v) denotes the degree of v in G. In this paper, we prove that every claw-free graph with edge weight at most 7 has strong chromatic index at most 9, which is sharp.
Keywords: strong edge coloring, strong chromatic index, claw-free graph, edge weight 
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Lin, Yuquan; Lin, Wensong. Strong chromatic index of claw-free graphs with edge weight seven. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 4, pp. 1311-1325. http://geodesic.mathdoc.fr/item/DMGT_2024_44_4_a4/